Over the past several months an adult patient has been treated for tetany. This condition is associated with an average total calcium level below 6 mg/dL. Recently, the patients total calcium tests have the following readings (in md/dl). Assume that the population of x values has an approximately normal distribution. 9.1 8.8 10.5 9.5 9.4 9.8 10.0 9.9 11.2 12.1 a: use a calculator with mean and standard deviation keys to find the sample mean reading x and the sample standard deviation s. Round to two decimal places. b: find a 99.9% confidence interval for the population mean of the total calcium in the patients blood. Round your answers to two decimal places lower limit upper limit
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Over the past several months an adult patient has been treated for tetany. This condition is associated with an average total calcium level below 6 mg/dL. Recently, the patients total calcium tests have the following readings (in md/dl). Assume that the population of x values has an approximately
9.1 8.8 10.5 9.5 9.4 9.8 10.0 9.9 11.2 12.1
a: use a calculator with
b: find a 99.9% confidence interval for the population mean of the total calcium in the patients blood. Round your answers to two decimal places
lower limit
upper limit
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